Turret damage

This article describes how damage from turrets is calculated. For general information on turret weapons, see Turrets. For information on how turrets function mechanically, see Turret mechanics.

This page should be updated due to game changes.
Reason: "parts into tracking" needs to be replaced with something new

Hit chance

A turrets chance to hit a target is calculated from the equation below. It will produce a result between 0 and 1, or 0% and 100% if you will. This value is then compared to a random number to see if the turret hits or misses.

[math]\pagecolor{Black}\color{White}\text{Chance to Hit} = {0.5^{\left({\left({\frac{V_{angular} \times 40000m}{WAS \times sig_{target}}}\right)^{2} + \left({\frac{max(0, Distance - opt_{turret})}{fall_{turret}}}\right)^{2}}\right)}}[/math]

V_angular is angular velocity (sideways movement between the attacker and the target, expressed as an angle (in radians) per second)

WAS is the turrets tracking value (listed on the info window) and means how well the turret can follow a moving target

sig_target is target signature radius (aka target size, a big target is easier to track)

distance is range to target in meters

opt_turret is optimal range of turret

fall_turret is falloff of turret

Click to enlarge

Those who like math may recognize that the hit chance equation has the form of x^(a+b), which can also be written as x^ax^b. In this case, x = 0.5, a = all tracking terms and b = all range terms. In other words, the hit chance equation can be thought of as having two separate parts (tracking and range), which are calculated individually and then multiplied at the end to get the final hit chance. This means that tracking and range don't interfere with one another, they are indeed two seperate things.

The equation also shows that the reduction of hit chance from falloff and tracking respectively follow the same pattern. This is because they both look like 0.5^{(something / x)2}, where x is either tracking or falloff. The only differance between them are the input values, the output is identical.

Example: At a range equal to optimal+falloff the range part of the equation becomes 0.5¹, which means a 50% chance to hit. Against a target with the same angular velocity (rad/s) as a turrets tracking value multiplied with the targets size and divided by 40000m, the tracking part of the equation becomes 0.5¹, which is also a 50% chance to hit. In the first case the full falloff range was used, in the second case the full turret tracking was used, and since they both follow the same pattern they end up at the same hit chance.

Falloff and optimal range

A target inside the optimal range of a turret will be hit 100% of the time, assuming no tracking is required.

Falloff is an additional range that goes beyond the optimal. Falloff is different than optimal in the sense that it reflects a gradual loss of hit chance. When a target is at optimal+falloff the hit chance is down to 50%. At optimal+(2 x falloff) the hit chance is down to 6.25%, but it's important to note that hits are still possible.

When using turrets that fight inside falloff ranges it can be useful to know that being at optimal+(falloff / 3) results in -11% average damage, being at optimal+(falloff / 2) results in -22% average damage and being at optimal+falloff results in -61% average damage (note: average damage falls faster than hit chance due to how the random damage interval is calculated, see below).

Falloff and optimal ranges are visible in the turrets info window. They are further modified by skills, ammo, modules, hull bonuses and incoming tracking disruptors. Target distance is visible on the overview.

Turret tracking

Tracking is a value that represents how well your turret can follow a moving ship. The equation is not fully realistic, it doesn't consider if the attacking ship is spinning around itself, it only considers the relative movement between the attacker and the target. This relative movement can from the attackers point of view be looked at as a change of the angle to the target, this angular velocity can be seen on the overview. But don't make the mistake of thinking that a turret can hit a target just because it can turn fast enough to follow the angular velocity of a target, it would be realistic if it could, but it's not how the equation works. Instead it behaves just like falloff, so when the turret turns as fast as the target moves, the chance to hit is 50%. This also means that the turret has a chance to hit a target that is moving faster than the turret can turn. With the updates to tracking it became easier to compare the tracking ability of turrets, but also a bit harder to understand how it works, since the turrets own turn speed is no longer visible and therefore hard to compare against the targets angular velocity that is visble in the overview. To get a turrets tracking value (in rad/s) that can be compared against to the targets angular velocity (in rad/s) the following equation must be used:

turret tracking in rad/s = Turret tracking x Target Signature Resolution / 40000m

There is of course no time or need to use math in combat. But it is helpful when one is trying to figure out what the actual effect a bonus or a penalty to tracking would have. As stated earlier, falloff and tracking follow the same behaviour, so a +10% bonus to tracking will have the same proportional impact on hitting a moving target, as would a +10% bonus to falloff have on hitting a target out in falloff range.

Turret tracking is visible in turret info window. It is modified by skill, ammo, modules, hull bonuses and incoming tracking disruptors.

A long, long time ago...
The "Turret Tracking" attribute in the formula used to be split into "Turret Tracking" and "Turret Signature Resolution". Combining them to single mumber simplified the formula without changing any mechanics. If you need to calculate turret hit chance with "Turret Signature Resolution" (for example using old NPC attribute info) just replace 40000 with "Turret Signature Resolution"

Angular velocity

This can be a tricky concept. Instead of measuring the speed as m/s or miles/hour, a speed can also be measured as the percieved change in the angle to an object from a certain location. A good example is the suns movement across the sky, where it moves 360° in 24 hours. If the sun is moving away or towards us is irrelevant, that wouldn't change the angle, only sideways movement will.

Just as a circle can be described as an angle of 360°, it can also be described as an angle of 2π radians. Meaning that one radian equals to (360/2π) roughly 57°.

The ingame overview can show the angular velocity of a target if you open the settings and tick a box under the tab called columns. Angular velocity is used to determine the penalty to the hit chance based on the turret's tracking ability. Relying on high angular velocities to stay alive is called speed tanking (not to be mixed up with kiting, which is to keep something at range). If an enemy is orbiting you, it is possible to use special maneuvers (like keep at range) or modules (like turning a web on and off) to try to mess with the angular velocity, this can make it easier to hit an otherwise hard to track target.

Angular velocity is calculated as ω=v_t/d, where v_t is tranversal velocity of the target relative to shooter and d is distance to target. The shooter and target will both have same angular velocity to each other.

Target Signature Radius

Every ship has a size that is treated as a sphere when they are being shot at. The target signature radius describes how big this sphere is. The signature radius is only used in the tracking part of the hit chance equation. So it only matters for tracking, it has no impact on the loss of hit chance due to long ranges.

Target signature radius is visible in ship fitting window. It is modified by modules, hull bonuses and incoming target painters.

Damage

The damage that a turret deal will be randomly spread around a fixed value called base damage. The base damage is calculated from the turret's Damage Multiplier attribute, the ammo's damage values, hull modifiers and skills.

Random damage interval

At the heart of each turret's damage output is a single randomly generated value between 0 and 1 that is several digits long. This random number is used both to determine if the turret hits the target and then to determine how much damage that hit actually did. If the random number is less than 0.01 (1% chance) it is a perfect hit and deals 300% of the base damage. A funny result of this is that when the hit chance is 1% or less, only misses and perfect hits can occur.

The damage modifier of the shot is calculated with the following formula, the first 0.01 of the random number interval is used for perfect hits which leads to a fixed damage modifier of x3:

Damage modifier = Random number[0.01,1] + 0.49

The base damage is multiplied by the damage modifier to get the final damage.

The combat log will show the quality of a hit as follows

Hit description	Random damage modifier
Barely scratches	0.500–0.625
Hits lightly	0.625–0.750
Hits	0.750–1.000
Well aimed	1.000–1.250
Excellent	1.250–1.490
Perfectly	3.000

Average damage

A turret with a hit chance of 100% will strike for 50% - 149% of its base damage in every non perfect hit. But since the same random number is used to determine a hit or miss as well as the damage modifier, this means that the upper damage interval will begin to shrink as well when the hit chance is decreased. The average damage is thus reduced in two ways, firstly by having some shots miss and deal no damage at all, and secondly by having the upper damage interval decrease as well. So the average damage will always be reduced more than the hit chance is.

Example: When the hit chance of a turret is 70% the damage interval has shrunk to 50% - 119% for all non perfect hits. When combined, these two things results in an average damage of just 61.3% (69%*(50%+119%)/2+1%*3) of the base damage.

Grouping guns, does it change the damage?

No. Even if the guns are grouped on your screen, they are still treated separately. This can be seen by collecting damage data and comparing that with the expected damage distribution, it's very clear that it's a combination of several separate turret shots instead of a single one. It can also be deduced by looking at the turret group's damage output when shooting at hard to hit objects, like things deep into falloff, it's then possible to tell when one, two or more guns hit the target.

Combined effects of hit chance and damage distribution

note: this seems redundant now, should probably be deleted

When a turret has less than 100% chance to hit the damage is reduced in two different ways. The first and obvious one is that it sometimes misses, the other is that the max damage on normal hits (e.g. not perfect ones) are reduced as well. Both of these effects will decrease the DPS output.

Since it was established earlier that Tracking and Falloff behave exactly the same way. We can use the same data table and the same graphs to describe both, but only one at the time.

The "Percent of Tracking or Falloff" values means how much of the listed falloff or tracking you are looking at. If your falloff is 12 km then 33.3% means one third of that, so 4 km. If your tracking is 0.4 rad/s then 50% would mean 0.2 rad/s.

The table below shows how damage and DPS goes down as a result of lower hit chance. The decrease is identical for tracking and falloff so either one can be used. If you wish to combine the effects of tracking and falloff, look them up individually and then multiply them (note: this only works for the columns Hit Chance and Relative DPS; the column Reduction in DPS by % can not be used for this).

The true strength with the table and graphs below are not to calculate what your DPS might be in a given situation. But rather to see how much you can push your falloff and tracking while still maintaining a decent DPS output.

Notes: Parts into means the value you multiply either your falloff or your tracking with. 0.25 means 25% or a quarter of that value. Likewise, the hit chance is expressed the same way. The relative DPS is a multiple to the base damage of the turret, it starts above 1 because of the perfect hits, since they do extra high damage.

Click to enlarge

Parts into Tracking or Falloff	Hit chance	Relative DPS	Reduction in DPS by %
0	1.0000	1.0151	0.0%
0.1	0.9931	1.0048	−1.0%
0.2	0.9727	0.9747	−4.0%
0.25	0.9576	0.9528	−6.1%
0.3	0.9395	0.9268	−8.7%
0.333	0.9260	0.9076	−10.6%
0.4	0.8950	0.8641	−14.9%
0.5	0.8409	0.7906	−22.1%
0.6	0.7792	0.7104	−30.0%
0.7	0.7120	0.6274	−38.2%
0.8	0.6417	0.5454	−46.3%
0.848	0.6075	0.5072	−50.0%
0.9	0.5704	0.4672	−54.0%
1.0	0.5000	0.3951	−61.1%
1.1	0.4323	0.3303	−67.5%
1.2	0.3686	0.2736	−73.0%
1.3	0.3099	0.2249	−77.8%
1.4	0.2570	0.1840	−81.9%
1.5	0.2102	0.1502	−85.2%
1.6	0.1696	0.1225	−87.9%
1.7	0.1349	0.1003	−90.1%
1.8	0.1058	0.0825	−91.9%
1.9	0.0819	0.0685	−93.2%
2.0	0.0625	0.0576	−94.3%
2.1	0.0470	0.0492	−95.2%
2.2	0.0349	0.0428	−95.8%
2.3	0.0256	0.0379	−96.3%
2.4	0.0185	0.0343	−96.6%
2.5	0.0131	0.0316	−96.9%
2.6	0.0092	0.0277	−97.3%
2.7	0.0064	0.0192	−98.1%
2.8	0.0044	0.0131	−98.7%
2.9	0.0029	0.0088	−99.1%
3.0	0.0020	0.0059	−99.4%

The formulas used to calculate this table were:

• Chance to Hit: 0.5^{(0+(falloff parts/1)2)}
• Relative DPS: if Hit Chance' > 0.01 then (Hit Chance − 0.01) × (0.50 + (Hit Chance + 0.49))/2 + 0.01 × 3, else Hit Chance × 3
• Reduction in DPS: (Relative DPS at Current/Relative DPS at 100% hit) × 100% − 100%

The best performance is up to 1/4 (quarter) of your falloff or tracking, the DPS loss is almost unnoticeable. At 1/2 (half) the DPS reduction is starting to be noticeable but it is still not too bad. Exactly at your falloff or tracking your DPS will be less than half, which is bad. As a rule of thumb, avoid using more than half of your falloff or tracking when you are trying to deal high damage.

Tracking upgrades vs Damage upgrades vs Target painter Vs Stasis webifier

note: unsure if this is helpful

Weapon upgrade modules can improve raw damage, tracking and range. Making use of an increased range is fairly obvious. However, comparing tracking and damage can be harder to do. The tricky thing with this comparison is that the need for tracking in a fight often varies depending on how the pilots fly their ships. So to make any sense of the following you must have some rough ideas of what the angular velocities will be. The only way to get that is through experience.

Here are some guidelines for comparisons: (note that only the bonus of the 1st module is considered for all tracking modules, additional ones will suffer from a stacking penalty).

Damage Upgrade module, T2 (such as Gyrostabilizer, Heat Sink etc):

• The 1st T2 Damage Upgrade module increase damage with +23.5%
• The 2nd T2 Damage Upgrade module increase damage with +20%
• The 3rd T2 Damage Upgrade module increase damage with +13%
• The 4th T2 Damage Upgrade module increase damage with +6.5%

Tracking Enchancer, T2:

• When Angular velocity = 25% of your Tracking: +9.5% more tracking is the same as +1.1% damage
• When Angular velocity = 50% of your Tracking: +9.5% more tracking is the same as +4.2% damage
• When Angular velocity = 75% of your Tracking: +9.5% more tracking is the same as +9.5% damage
• When Angular velocity = 100% of your Tracking: +9.5% more tracking is the same as +16.6% damage

Tracking Rig, T1:

• When Angular velocity = 25% of your Tracking: +15% more tracking is the same as +1.5% damage
• When Angular velocity = 50% of your Tracking: +15% more tracking is the same as +6.3% damage
• When Angular velocity = 75% of your Tracking: +15% more tracking is the same as +14.3% damage
• When Angular velocity = 100% of your Tracking: +15% more tracking is the same as +25.4% damage

Tracking Computer, T2 with tracking script:

• When Angular velocity = 25% of your Tracking: +30% more tracking is the same as +2.7% damage
• When Angular velocity = 50% of your Tracking: +30% more tracking is the same as +10.8% damage
• When Angular velocity = 75% of your Tracking: +30% more tracking is the same as +25.2% damage
• When Angular velocity = 100% of your Tracking: +30% more tracking is the same as +46.7% damage

Target Painter, T2 with Signature Focusing at level IV (increasing sig radius have the exact same result on damage as an increase in tracking has)

• When Angular velocity = 25% of your Tracking: +36% higher sig radius is the same as +3.0% damage
• When Angular velocity = 50% of your Tracking: +36% higher sig radius is the same as +12.3% damage
• When Angular velocity = 75% of your Tracking: +36% higher sig radius is the same as +28.8% damage
• When Angular velocity = 100% of your Tracking: +36% higher sig radius is the same as +54.1% damage

Note that a target painter helps everyone who shoots at the targetwhile damage/tracking upgrades help only one ship.

Webs:

The effect from a web is hard to predict, since its use can change both the transversal speed and the range between the ships. Experience and practice will be your best guide here. The drawback with webs is that they can help your opponents tracking as well as your own. The web is more often used for its tactical benefits, such as giving control over the range. But it is also the best tool to reduce the need for tracking when large guns are used against small targets. Stasis webifier alsoo has limited range compared to other modules.

Choosing turrets

note: should be rewritten

Is it better with high damage or high tracking turrets? It is almost always better to go for the highest possible damage, which also gives a higher range. This is true for long range (like artillery) and short range (like autocannons) guns alike. The reason for this is because the gain in tracking isn't enough to compete with the lost damage.

The only turret type where higher tracking can possibly outweigh the extra damage and range is for autocannons, the other types simply don't gain enough tracking to be worth even looking into. The lighter autocannon type has +32% tracking, −23% damage and −17% falloff compared to the heavier type (for small, mediums and large alike). The following example will compare heavy vs light, there will be lots of numbers, but there is a summary at the end of it of it all if you want to skip ahead.

Example: This is a comparison of when the lighter type overtakes the heavier type against a target with high angular velocity. For this example it is assumed that the range is same in both cases so that the angular velocity will be identical. A pilot is using the heavier autocannons (for example small 200 mm, but this comparison is true for medium and large as well) and is fighting at 0.333 parts into falloff (corresponds to about 2200 m with hard hitting ammo and T2 guns (for T1 it would be 2100 m, so no real difference)), this corresponds to a 10% DPS loss from range, tracking isn't considered yet. If the pilot instead had been using the lighter autocannons (small 125 mm) the range is the same (2200 m for T2 guns) but this time it corresponds to 0.4 parts into falloff where the DPS loss from falloff is 15%. Now we will compare the guns damage output, we must remember that the lighter version does −23% damage as well. So in this range case the relative DPS from the heavier one is 0.90 and for the lighter it is (0.85 × 0.77 =) 0.655, we can divide them (0.9/0.655) to find out that the heavier ones do 37% more DPS over the lighter ones. Now the question is, at how many parts into tracking will these guns do the same damage? Since the lighter ones track better, the heavier ones will lose DPS faster and we are looking for the point where they do the same damage. It turns out that when the heavier type is at 0.9 parts into tracking, they lose 53% DPS, at the same time the lighter version is only 0.68 parts into tracking (0.9/1.32, 32% faster tracking), where it loses 36% DPS. Comparing the relative DPS we get that the lighter do 0.64 and the heavier 0.47, we divide them (0.64/0.47) and see that the lighter ones do 36% more DPS (from just tracking) at this point. This is close to the 37% advantage that the heavier had from before.

Summary: Only when the heavier autocannons get near 1.0 parts of their tracking, will the lighter ones start performing better. At this point, the drop in DPS is already big (like half). It is therefore generally more useful to fit the heaviest type you can and then fly in a way that reduce the demand for tracking if need be. Lighter weapons are mostly only useful when a ship uses up its CPU and PG on other things.

References

http://forum.eveuniversity.org/viewtopic.php?p=201888#201888

http://forum.eveuniversity.org/viewtopic.php?p=216525#p216525

http://www.hostile.dk/files/eve/eve-tracking101.swf

https://www.reddit.com/r/Eve/comments/5h24bk/turrets_listed_signature_resolution_is_40km/